RESTRICTED MAXIMUM LIKELIHOOD ESTIMATION FOR MULTIVARIATE LINEAR MIXED MODEL IN ANALYZING PISA DATA FOR INDONESIAN STUDENTS

The Program for International Student Assessment (PISA), becomes one of the references or indicators used to assess the development of students' knowledge and skills in each member country of the Organization for Economic Cooperation and Development (OECD). The results of the PISA survey in 2018 placed Indonesia in the bottom 10, indicating that the implementation of the national education system has not been successful. This underlies the need for a more in-depth study of the factors that influence PISA data scores not only statistically qualitatively but also quantitatively which is still very rarely done. The data structure of the PISA survey results is complex, which involves multicollinearity, multivariate response variables, and random effects. Thus, it requires an appropriate statistical analysis method such as the multivariate mixed linear regression (MLMM) model. In this study, secondary data from the results of the 2018 PISA survey with Indonesian students as the smallest unit of observation were used as sample. School is used as an intercept random effect which is assumed to be normally distributed. Multicollinearity is overcome by selecting independent variables based on AIC and BIC values. Estimation of variance and random effect parameters was performed using the restricted maximum likelihood (REML) method. Based on the estimator of the variance of random effects for the response variables of mathematics, science, and reading literacy, it was obtained 1548.12, 1359.39, and 1082.48, respectively, which explains the significant effect of each school as a random effect on the three response variables